real crystals, crystal defects · point defects real crystals, crystal defects 4/34. vacancy real...
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Real crystals, crystal defects
Real crystals, crystal defects 1/34
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• The strength of real metals is less than 1% than
that of calculated from ideal crystal models
• Doping Si with 10-8 weight percent Boron increases its conductivity by two-times
• CRYSTAL DEFECTS
REAL CRYSTALS
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• Point defects (0 dim.)
• Line defects (1 dim.) dislocations
• Surface defects (2 dim.)
• Volume defects (3 dim.)
CRYSTAL DEFECTS
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• Vacancy (empty lattice space)
• Self interstitial atoms
• Foreign atoms (interstitial or substitutional
places)
POINT DEFECTS
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VACANCY
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The vacancy is the
absence of an atom from
the lattice. The attractive
and repulsive forces
acting on the neighboring
atoms are changed, so
lattice distortion is
produced in the
environment of the
vacancy.
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SUBSTITUTIONAL ATOM
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The substitutional atom is
a foreign atom in the
lattice. The attractive and
repulsive forces acting on
the neighboring atoms are
changed, so lattice
distortion is produced in
the environment of the
atom.
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INTERSTITIAL ATOM
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The interstitial atom is a
foreign atom between the
regular lattice positions.
The attractive and
repulsive forces acting on
the neighboring atoms are
changed, so lattice
distortion is produced in the
environment of the atom.
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FRENKEL-MECHANISM
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Due to high energy
interaction (e.g. particle
irradiation) an atom left the
lattice site leaving a
vacancy behind and mode
into an interstitial position.
It causes extreme lattice
distortion.
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WAGNER-SCHOTTKY MECHANISM
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Atoms leaving the free surface, and atoms jump from the
interior to their place. In this way a vacancy diffuses trough
the lattice into the materials interior.
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• Radiation– Atoms are moved out of the regular lattice position (e.g.
Frenkel-pair)
• Heat
nü: number of empty lattice sites
N: number of lattice sites
Qü: activation energy
k: Boltzmann constant
T: temperature
POINT DEFECTS
Point defect density
Exponential
curve
slope
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POINT DEFECTS IN ALLOYS
Solid solution: base metal (A) + solved atom (B)
Substitutional alloy
e.g. Cu + Ni
interstitial alloy
e.g. Fe + C
Second phase in solid solution
or
Second phase particle
different chemical composition
different structure
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EFFECT OF POINT DEFECTS
Aluminium Copper
Strain (%) Strain (%)
Str
ess (
MP
a)
Str
ess (
MP
a)
softSlow cooling
quenchingNeutron irradiated
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• Large difference between theoretical and
measured flow stress of metals.
• Dislocation theory: plastic deformation does not
happen in one step → dislocation motion
DISLOCATIONS (1 D)
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2 (1 )
merőleges
párhuzamos
E
G
E G
Poisson coefficient
(ε - strain)
Tensile stress
Shear stress
MECHANICAL PROPERTIES
perpendicular
parallel
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• Assumption: during the deformation the crystal planes slip in one step relative to each other by simultaneous motion of the atoms.
• The stress what is necessary to start the plastic deformation calculated this way is 1-2 order of magnitude higher than the measured values.
• Conclusion: during the plastic deformation the slip of crystal planes don’t occur in one step, but through a continuous motion; that is, there are regions where the slip already occurred, and others where didn’t.
• The lines separating this regions are called dislocations.
THEORETICAL YIELD STRESS
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DISLOCATIONS MOTION
The analogy between
the dislocations and
the caterpillar
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BURGERS-CIRCLE
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In a defect-free lattice starting from a lattice position and
stepping the same distance to right, down, left and upward,
we return to the starting point.
If the crystal contains a dislocation, the starting and end
point will be different. The vector connecting them is the
Burgers-vector.
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Dislocation line: l
Slip plane.
→fixed
Burgers vector: b
b l,
The line of the
dislocation and the
elemental deformation
caused are
perpendicular.
EDGE DISLOCATION
Extra half plane
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Dislocation line: l
Burgers vector: b
Slip plane is not fixed
→glissile
No extra half plane!
b II l, The line of the
dislocation and the
elemental deformation
caused are parallel.
SCREW DISLOCATION
The axis of the screw dislocation
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Partial slip
A line in the space
0-90°
The angle between the line of the
dislocation and the elemental
deformation it causes is between 0
and 90°.
COMPOSITE DISLOCATION
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• Dislocation: border of slipped and non-slipped regions
• Linear defect
• Starts and ends on a crystal surface, ore forms a
closed loop
• Plastic deformation along the whole dislocation is
constant
• Burgers vector is in the closest packed plane and
direction, and b = d
Real crystals, crystal defects 21/34
BASIC PROPERTIES OF DISLOCATIONS
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• Macroscopic surface
• Small angle grain boundary
• High angle grain boundary
• Phase boundary
• Coherent phase boundary
• Twin boundary
• Stacking fault
PLANAR DEFECTS
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• Atoms on the surface are at higher energetic state than in
the crystal interior, because there are no atomic bondings
at every directions.
• Surface energy decreases if additional atoms join the
surface.
• Oxide layer formation.
• Chemical reactions.
MACROSCOPIC SURFACE
surface
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Dislocations are arranged
below each others
SMALL ANGLE GRAIN BOUNDARY
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The angle difference of the
orientation of the regions separated
by small angle grain boundaries:
< 5°
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During solidification the
randomly oriented grains
touch each other. Grains
differ from each other
only in orientation.
HIGH ANGLE GRAIN BOUNDARIES
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SMALL AND HIGH ANGLE GRAIN BOUNDARIES
Surface
energy
Small angle grain boundary High angle grain boundary
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PHASE BOUNDARY
Coherent
Low energy surface defectSemicoherent
Incoherent
High energy
surface defect
phase boundary
Phase
boundary
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• Atoms on the two sides of the boundary are similar
• There can be found a plane in both phases where the
atomic arrangement is similar
• Orientation difference is fixed on the phase boundary
COHERENT PHASE BOUNDARY
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• Coherent boundary, separates
similar phases
• The two sides of the boundary
are mirror images
• It can be formed during
crystallization or plastic
deformation in FCC or HCP
materials
TWIN BOUNDARY
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Parallel lines in a
microscopic image
TWIN BOUNDARY
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Due to missing
atoms (internal
stacking fault)
the stacking order of
atomic layers is
locally changed.
STACKING FAULT
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Due to included extra
atoms (external stacking
fault)
the stacking order of
atomic layers is locally
changed.
STACKING FAULT
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• Cavities
• Inclusions
• Precipitations
• Gas bubbles
VOLUME (3 DIM.) DEFECTS
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CAVITIES
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Cavities along grain boundaries.
Scanning electron microscope image.